Correct option is D
Given:
There are 20 two-digit numbers.
One number was entered incorrectly by interchanging its digits.
Because of this, the average decreased by 1.8
We need to find the difference between the digits of the number that were interchanged.
Solution:
Step 1: Let the correct number be 10a + b
(a is the tens digit, b is the units digit)
When digits are interchanged, the number becomes: 10b + a
So, the difference in value caused by the mistake =
(10a + b) – (10b + a) = 9a – 9b = 9(a – b)
Step 2: Since average decreased by 1.8 across 20 numbers
Total decrease = 1.8 × 20 = 36
So,
9(a – b) = 36
a – b = 36 / 9 = 4
Final Answer: (d) 4
